Maximum particle displacement in a sonic boom wave

In summary, to find the maximum particle displacement for a typical sonic boom, the equation ParticleDisplacement = SoundPressure / (SpeedOfSound*AirDensity*2*PI*SoundFrequency) can be used, where the speed of the wave (u) is represented by the equation u = p * C0 * rho0 or u = c0 * S, and the formula velocity = wavelength * frequency can be used to bring together the velocity of the wave, its wavelength, and its frequency. The units should also be checked when using these equations.
  • #1
markmai86
7
0

Homework Statement



A typical sonic boom is a solitary N wave with a peak to peak pressure amplitude of 2 lbf/ft^2 and a wavelength of 50 ft. Find the maximum particle displacement.


Homework Equations



None

The Attempt at a Solution



I've found some equations on the internet. For instance, I have the speed of the wave (u) (that I should then differentiate to get the particle displacement I think...):
u = p * C0 * rho0
or
u = c0 * S
I can't manage anyhting with these equations and I can't find anything representing the sound wave of the problem on a graph. I can't visualize the problem at all.
Could anyone give me some tips or explanations on this problem?

Thank you
 
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  • #3
Carid said:
I found this expression here

http://en.wikipedia.org/wiki/Particle_amplitude

ParticleDisplacement = SoundPressure / (SpeedOfSound*AirDensity*2*PI*SoundFrequency)

Thank you for the formula, but this formula includes the Sound frequency and the sound pressure which are not in the problem statement. Is it something I should know or I could find on the internet?

Thank you
 
Last edited:
  • #4
Do you know any formula which brings together the velocity of a wave, its wavelength and its frequency?

As for pressure, doesn't the question include this information?
 
  • #5
Sorry about the sound pressure, I wrote that maybe a little too fast.

As for the formula you are talking about is it:

velcity = wavelength * frequency

?
 
  • #6
Yes, that's the one:approve:
 
  • #7
Alright I think everything is working out, I'll just have to check the units as I'm not very familiar with it.

Thank you very much
 

1. What is maximum particle displacement in a sonic boom wave?

Maximum particle displacement in a sonic boom wave refers to the maximum distance that particles in the air are displaced from their original position as a result of a sudden change in air pressure caused by a supersonic object.

2. How is maximum particle displacement in a sonic boom wave measured?

Maximum particle displacement in a sonic boom wave is typically measured in units of pressure, such as pounds per square inch (psi), using specialized instruments called microphones or pressure sensors.

3. Can maximum particle displacement in a sonic boom wave cause damage?

In most cases, maximum particle displacement in a sonic boom wave is not strong enough to cause any significant damage to structures or objects. However, in rare cases, it can cause minor damage to windows or fragile objects.

4. What factors can affect the maximum particle displacement in a sonic boom wave?

The maximum particle displacement in a sonic boom wave can be influenced by a variety of factors, including the speed and altitude of the supersonic object, the atmospheric conditions, and the distance from the source of the sonic boom.

5. How can maximum particle displacement in a sonic boom wave be reduced?

There are several methods that can be used to reduce the maximum particle displacement in a sonic boom wave, including designing aircraft with more aerodynamic shapes, using noise-reducing materials, and flying at higher altitudes.

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